4.5.5 - Uniformity Measurements

The Flux Simulator provides some statistical indicators to measure the uniformity of the read distribution along a transcript produced by in silico sequencing.

The fraction of a transcript that is covered by reads reflects its expression and the degree of of coverage fluctuation provoked by biases.

$//<![CDATA[ \begin{array}{l}\sum \limits_{i=1}^L \frac{sgn(cov(i))}{L}\end{array} //]]>$ where $//<![CDATA[ \begin{array}{l}L\end{array} //]]>$ is the length of the transcript,

and the sign function

indicating whether a position is covered by at least one sequenced read.

Pearson’s chi-square can be used to test the goodness of fit of a given sample to a theoretical distribution. Given a transcript of length $//<![CDATA[ \begin{array}{l}L\end{array} //]]>$ and coverage $//<![CDATA[ \begin{array}{l}cov(i)\end{array} //]]>$ at position $//<![CDATA[ \begin{array}{l}i\end{array} //]]>$, the test statistic is defined as follows:

where $//<![CDATA[ \begin{array}{l}\mu = \sum\limits_{i=1}^L \frac{cov(i)}{L}\end{array} //]]>$ is the average coverage along the molecule.

A CV is defined as the ratio of the standard deviation and the standard deviation of a probability distribution:

$//<![CDATA[ \begin{array}{l}\textrm{CV}= \frac{\sigma}{\mu}\end{array} //]]>$, with standard deviation $//<![CDATA[ \begin{array}{l}\sigma= \sqrt{\sum\limits_{i=1}^L \frac{(\overline{cov}(i))^2}{L}}\end{array} //]]>$ and mean  $//<![CDATA[ \begin{array}{l}\mu= \sum\limits_{i=1}^L \frac{\overline{cov}(i)}{L}\end{array} //]]>$

of transformed coverage values $//<![CDATA[ \begin{array}{l}\overline{cov}(i)= \frac{3}{2} \left(\frac{cov(i)^{\frac{2}{3}}-\mu^{\frac{2}{3}}}{\mu^{\frac{1}{6}}}\right)\end{array} //]]>$

Latter Anscombe transformation of coverage values has been proposed [Hansen et al. 2010] under the assumption that the distribution of reads along a transcript follows a Poisson distribution, which is to be transformed to a Gaussian distribution.